question_answer

Find the unknown angle y in the figure. \[{{t}_{1}}||{{t}_{2}}\]

A)  \[45{}^\circ \]                      

B)  \[125{}^\circ \]          

C)  \[90{}^\circ \]                      

D)  \[80{}^\circ \]

Correct Answer: B

Solution :

(b): Draw \[{{t}_{3}}||{{t}_{1}}\] from point 'R' Construct a line \[{{t}_{3}}\] through R and parallel to \[{{t}_{1}}\] & \[{{t}_{2}}\]. \[\Rightarrow \,\,\,a+b=y\]  and \[a=45{}^\circ \] (Corresponding angles) \[b=180{}^\circ -100{}^\circ =80{}^\circ \] (Angles on the same side of transversal.) \[\Rightarrow \,\,y=a+b=45{}^\circ +80{}^\circ =125{}^\circ \]